Question

Occasionally, people can survive falling large distances if the surface they land on is soft enough. During a traverse of Eiger's infamous Nordvand, mountaineer Carlos Ragone's rock anchor gave way and he plummeted 488 feet to land in snow. Amazingly, he suffered only a few bruises and a wrenched shoulder. Assuming that his impact left a hole in the snow 4.5 ft deep, estimate his average acceleration as he slowed to a stop (that is while he was impacting the snow). (Note, for this question the positive direction is defined as down.)

Answer 1

The velocity just before he touches the snow is given by $v_1$

Now,

using equation of motion for his free fall to snow

$v_1^2-u^2=2a_1s_1$

$u=0$

$a_1=9.8\frac{m}{sec^2}$

$s_1=488ft=148.742m$

Hence,

$v_1=$ $54\frac{m}{sec}$

Now,

using equation of motion for decceleration by snow

$v^2-{v_1}^2=2a_2s_2$

$s_2=4.5ft=1.3716m$

$v=0$

Solving it we get,

$a_2=-1063\frac{m}{sec^2}$

his average acceleration as he slowed to a stop is $1063\frac{m}{sec^2}$